Home
Class 12
MATHS
If 2p^3 - 9pq + 27r = 0 then prove that ...

If `2p^3 - 9pq + 27r = 0` then prove that the roots of the equations `rx^3 - qx^2 + px - 1 = 0` are in H.P.

Promotional Banner

Topper's Solved these Questions

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-1 (PART -1: PRE RMO) |46 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-1 (PART -II: RMO) |9 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos
  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos
  • FUNDAMENTAL OF MATHEMATICS

    RESONANCE ENGLISH|Exercise Exercise|135 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

If the roots of the equation x^(3) + bx^(2) + 3x - 1 = 0 form a non-decreasing H.P., then

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P then 2q^3 =9r (pq-3r)

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in A.P 2p^3 - 9 pq + 27 r=0

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

Solve the equation 6x^3 -11x^2 +6x -1=0 the roots being in H.P

If the sum of two roots of the equation x^3-px^2 + qx-r =0 is zero, then:

The condition that the roots of x^3 +3 px^2 +3qx +r = 0 may be in H.P. is

The roots alpha, beta and gamma of an equation x^(3) - 3 a x^(2) + 3 bx - c = 0 are in H.P. Then,

If the roots of 24x^3 - 26 x^2 + 9x -1=0 are in H.P then the roots are

RESONANCE ENGLISH-EQUATIONS -SELF PRACTICE PROBLEMS:
  1. For what value of k ,(4-k)x^2+(2k+4)x+(8k+1)=0 is a perfect square.

    Text Solution

    |

  2. If (x - a) be a factor common to a(1)x^(2) + b(1)x +c and a2x^2 + b(2...

    Text Solution

    |

  3. If 3x^(2) + 2alphaxy + 2y^(2) + 2ax - 4y+1 can be resolved into two li...

    Text Solution

    |

  4. Let 4x^2 - 4(alpha - 2)x + alpha - 2 = 0 (alpha in R) be a quadratic e...

    Text Solution

    |

  5. If P(x) = ax^(2) + bx + c, and Q(x) = -ax^(2) + dx + c, ax ne 0 then p...

    Text Solution

    |

  6. If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common...

    Text Solution

    |

  7. If ax^2 + 2bx + c = 0 and x^2 + 2b(1)x + c(1) = 0 have a common root a...

    Text Solution

    |

  8. If 2p^3 - 9pq + 27r = 0 then prove that the roots of the equations rx^...

    Text Solution

    |

  9. If a, c gt 0 and ax^2 + 2bx + 3c = 0 does not have any real roots the...

    Text Solution

    |

  10. If f(x) =(x-a) (x-b), then show that f(x) ge (a-b)^(2)/4

    Text Solution

    |

  11. Find the least integral value of 'k' for which the quadratic polynomia...

    Text Solution

    |

  12. Find the range of the expression (x^(2) + 34x - 71)/(x^(2) + 2x -7), i...

    Text Solution

    |

  13. Find the interval in which .'m' lies so that the expression (mx^(2) + ...

    Text Solution

    |

  14. Find the value of b for which difference between maximum and minimum v...

    Text Solution

    |

  15. Find all numbers a for each of which the least value of the quadratic ...

    Text Solution

    |

  16. Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then ...

    Text Solution

    |

  17. Find the values of p for which both the roots of the equation 4x^2 - 2...

    Text Solution

    |

  18. Find all values of p so that 6 lies between roots of the equation x^(2...

    Text Solution

    |

  19. Let x^2 - 2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then...

    Text Solution

    |

  20. Find the values of a, for which the quadratic expression ax^2 + (a - 2...

    Text Solution

    |